Science, Technology, Engineering, and Math

MICHAEL HEIZER United States, b. 1944 Levitated Mass, 2011 Granite, concrete, and steel; 258 x 5472 in. Zenith: 180 in., Weight: 340 tons LACMA © Michael Heizer (M.2011.35)

TEM (science, technology, engineering, and the collection of the Los Angeles County Museum math) Education may be a newly named of Art can provide the basis for lesson plans that Sinitiative, but these content areas have always have the potential to broaden student thinking in been at the core of the K–12 curriculum. As soon all of these subjects. The key question addressed as the acronym “STEM” was conceived, artists and in this packet is: How do artists connect math, museums raised the issue of where the arts come engineering, and technology to make art? This into play, expanding the initiative to “STEAM.” curriculum connects initiatives that cross into STEAM and its application to K–12 classrooms the museum and the classroom by placing art- highlight the relationship between artistic, mathe- works in conversation with what are often matical, and engineering practice. Artworks from considered “hard” subjects.

______

Just as STEAM is a newly named initiative that Line of Inquiry: A series of open-ended questions revisits older ideas in a contemporary way, that navigate exploration of the essential question Project-Based Learning, or PBL, is a reconception and practice with core content. Stages include of longstanding pedagogy in a project-based brainstorming, mapping of tasks, and generating approach. The units included here are presented possible solutions. in this format, and each is formulated to support student inquiry in math and engineering through Equal Voicing: Various roles (chosen by either the language of the visual arts and principles of the student or the educator, depending on age or design. learning needs) that provide opportunities for individual and collaborative contributions. Educators have long valued teaching that emphasizes learning while doing in contexts Revision: Editing prompts to encourage inspired by real-world situations. PBL supports adjustments in research or improvements to the this philosophy by placing the student at the final product. center of his/her own learning, empowering students to propose questions, direct research, Presentation: A forum that allows students to and interpret answers. The educator acts as a share their research with classmates, the school, guide through exercises in exploration, the neighboring community, or practitioners in experimentation, revision, and reflection. The the field. process is the focus, rather than the culminating project, which requires educators to relinquish Reflection: Students state their accomplishments some control over the end product. Teachers through formative assessment and cumulative learn alongside students as they cooperatively self- or group-evaluation. Reflection recalls the define the project, utilizing a combination of use of problem-solving and persistence. direct instruction and open-ended questioning. The artworks featured in this curriculum serve as In PBL, teaching and learning take the form of engaging entry points into math and engineering an extended experience comprising key tenets. concepts. Use the information and images provided to facilitate an initial conversation or Point of Entry: An introductory activity such interaction with an artwork through questions as a field trip, discussion, or demonstration that such as, “What do you see?” “What do you see can be inspired by literature, journalism, media, that makes you say that?” and “What more can or art. you find?” The essential questions that follow serve as extensions into PBL experiences, and, in Essential Question: A driving question that this case, students should utilize the languages of frames the unit and guides student thinking mathematics and the visual arts to answer such throughout the process. questions. Suggested grade levels are aligned with content standards that can be scaffolded and Core Content: Curricular concepts that integrate adapted for students. learning across subject areas.

Urban Light, 2008, Chris Burden ______

CHRIS BURDEN United States, b. 1946 Urban Light, 2008 1 1 1 202 restored cast-iron antique street lamps, 320 /2 x 666 /2 x 704 /2 in. LACMA, the Gordon Family Foundation’s gift to Transformation: The LACMA Campaign © Chris Burden (M.2007.147.1–.202)

Chris Burden, an L.A.-based artist interested in The lights that populate this work were collected contemporary life and the urban experience, has over a seven-year period, and each individual spent much of his career exploring the intersection lamp represents the unique time and place of its of art and engineering, employing construction original location. For example, the seventeen materials and found objects to create large-scale lamps from Lynwood are each twelve feet tall and sculptures such as Urban Light. For Urban Light, simple in design, with a single light globe. The six Burden utilized a collection of 202 antique street from Glendale stand at nineteen feet and feature lamps from the city of L.A. circa the 1920s and double globes and a decorative design. All 202 '30s. Their installation, arranged carefully on a lamps have fluted shafts or trunks in the form of grid, exemplifies the real-world nexus of math, prisms, and all are painted grey. The street lamps art, and design. are grouped in rows according to neighborhood, and the arrangement forms a grid that (despite initial appearances) is not perfect—but does offer repetition of shape and color.

CHRIS BURDEN United States, b. 1946 Diagrams of Urban Light, 2007 © Chris Burden Studio

Write an algebraic expression to describe the total Point of Entry: Planning for the sculpture’s number of globes (y) as it relates to the number of installation paralleled the planting of a garden. lampposts (x). Use a coefficient of 1, 2, or 3 to The lampposts were first measured for height, distinguish single-, double-, and triple-globed weight, and square base. Similar to how one might posts. If you were to design a school garden organize flowers, the artist grouped the lamps inspired by this artwork, how would you map the according to their unique designs, such as single, arrangement of flowers and plants, and why? (symmetrical) double, or (rotationally symmetrical) triple globes. Rows were arranged by height. The Equal Voicing: How will you work in teams to tallest posts comprise the middle section and are execute the garden? Students may take roles: flanked by the shortest posts to create the effect botanists to research plants and their character- of a symmetrical pyramid. From the perspective istics; mathematicians to determine the distance of the street, this allows the viewer to see all of between two plants and where seeds should be the lamps at once. In the practice of gardening, planted by plotting the plants on a grid; and, a similar arrangement ensures that the shortest finally, gardeners to realize the design. and tallest plants receive equal amounts of light. Revision: What other ways could you group the Essential Question: How can you use symmetry plants? How can you arrange them so that they and scale to beautify the school? all receive equal amounts of sunlight? Where on campus will you plant the garden? How much Grades: K–4 space will it require?

Core Content: Line, shape, pattern, motif, form, Presentation: Unveil the gardens in a ribbon- scale, polygonal prism, symmetry (bilateral and cutting ceremony for the school. Present your rotational), algebraic expression, and space. research, such as information on the various garden habitats, at an accompanying science fair. Line of Inquiry: What do you see in Urban Light? Ask students to present their findings to When you look closely, what shapes, patterns, or classmates and peers. motifs do you notice? How would you describe the bases and columns in geometric terms? When you Reflection: How do people practice math in take an overall view, what type of lines emerge? everyday life? What is the relationship between How does the sculpture’s arrangement form a math and design? If you were to design the two-dimensional grid and a three-dimensional garden again, what parts of the process would pyramid? How are the lampposts grouped? How you repeat? What would you do differently, or many globes do you see in each group? what changes would you make? Where could you plant another garden?

Metropolis II, 2010, Chris Burden ______

CHRIS BURDEN United States, b. 1946 Metropolis II (detail), 2010 3½ hp DC motors with motor controllers, 12,000 custom manufactured die-cast cars (1,100 for operating, 10,900 for replenishing damaged cars), 26 HO-scale train sets with controllers and tracks (13 for operating,13 for replenishing damages), steel, aluminum, shielded copper wire, copper sheet, brass, various plastics, assorted woods and manufactured wood products, Legos, Lincoln Logs, Dado Cubes, glass, ceramic and natural stone tiles, acrylic and oil-based paints, rubber, and sundry adhesives; 117 x 339 x 230 in. © Chris Burden. Courtesy Gagosian Gallery. Photography by E. Koyama. (L.2010.33.1)

In addition to large-scale objects, Burden is also The energy starts at the center of the sculpture, an avid collector of miniatures, and has employed where the conveyor belt magnets carry six lanes them to create imaginative works such as of cars to a seven-and-a-half foot peak. The cars Metropolis II. A model city composed of cars, are lined up in rows, and each follows a distinct trains, and buildings, Metropolis II is a maze of and specific path. Attempting to follow a single speed and sound. Eleven hundred Hot Wheels- car with the eye can be dizzying; if they were size cars and thirteen miniature passenger trains full-size cars they would be traveling at 240 race through 1,350 feet of track. Twenty-five miles per hour. skyscrapers dot the horizon, interwoven with two freeway ramps and eighteen lanes of traffic.

ZAK COOK United States, b. 1969 Map of Metropolis II, 2010 © Chris Burden Studio. Photo © Zak Cook.

Designer Zak Cook worked with Burden and a Finally, the string tracks were marked with pen team of artists to build Metropolis II. The planning at five-foot-scale increments to help the artists phase, mapping, was accomplished with simple transform a two-dimensional representation into string and pen. The sculpture’s footprint, or a three-dimensional sculpture. overall length and width, were first determined based on the dimensions of the magnetic The boxes that would eventually transport the conveyors. A core base was mapped out at seven sculpture were seven and a half feet tall, so Cook by twenty-two feet to scale. Designers added set the maximum height of the sculpture at seven extensions and corners to the basic rectangular and a half feet. With the tallest peak in mind, he shape to alter the direction of the cars’ eventual experimented with the slope of the tracks and travel routes. In terms of dimensions, special figured that a slope of five and a half degrees consideration was given to the fact that the final would produce an ideal speed. Cook used the sculpture would not remain in Burden’s studio Pythagorean theorem to determine the width of and would need to be shipped—and likely many construction (one and one-eighth feet of fall per times—to exhibition sites. Cook decided where linear foot of travel), and artists built to this the different parts of the base would separate, dimension. Designers worked out individual creating seam lines so that all parts would be curves using curve templates, and track walls removable and replaceable for both assembly and were beveled by hand for fluid travel. They tested disassembly. Within the footprint, Cook mapped the cars on the tracks, placing brushes before and out a series of track configurations using colored after significant curves to avoid crashes. Lastly, string to code track groupings. The goal of the support structure was “sketched out” by mapping the tracks was to maximize the number positioning metal frames in different combina- of tracks that could assemble onto the two- tions. Cardboard mockups of buildings were dimensional footprint, considering the width of added in as layers, and final buildings took the track groupings as outer tracks would be longer form of wooden replicas (and one paper original) and the inner tracks shorter. Designers also of the children’s game House of Cards by 1950s mapped both right and left curves to create designers Charles and Ray Eames, as well as tiled balance in the overall direction of travel. ceramic, mirrored, and metallic buildings.

Point of Entry: The relationship between the How can you alter the tracks to control the speed sculpture’s vehicles, roads, and buildings and of travel? Map the course of the track on a the process the artist went through to create it coordinate plane. Now, how will you transform resemble a city-planning experiment. City a two-dimensional map into a three-dimensional planners use design principles and engineering city? tools to create environments that connect people with buildings, transportation, and the surround- Equal Voicing: How will the class work together ing urban landscape. With technology, they to build the city? Assign roles that include city create designs that impact the real world. Use planners to map the space, engineers to design accessible and recyclable materials to create your the roadways, architects to imagine mixed-use own classroom city. structures, and mathematicians to help preparators take the map to scale. Essential Question: How do artists and designers practice engineering in everyday life? Revision: Where will the support structures go? How should they be configured and why? Where Grades: 4–8 do marbles fly off the tracks? Reduce the angle of descent to slow the rate of travel, or add a Core Content: Length, height, and width; square textured material such as brushes to slow the footage; cubic feet; ratio; slope; radius; and velocity. marbles at key trouble spots. Finally, how will you layer buildings into the structure for Line of Inquiry: What is the first thing you aesthetic effect? What household and recycled notice about Metropolis II? What do you find materials will you source to construct the following a closer look? Does the sculpture look buildings? like a representation of the past, present, or future? What do you see that makes you say that? Presentation: Conduct a series of test runs in Describe the size of the work and the speed of the the school auditorium for lower-grade audiences. cars. Present a series of accompanying poster boards that scaffold the construction process down into What impact does a model version like this have digestible steps comprehendible for younger on the “life” of the city? What types of vehicles, students. After receiving feedback from students buildings, and infrastructure would you include and teachers, invite local engineers and city in your own unique city? For what purposes and planners to a special viewing. Ask groups of functions? How would they be used in relationship students to talk about how the creators’ different to one another? roles contributed to the overall process.

Determine the footprint of your classroom city, Reflection: What are the real-world professions starting with a simple rectangular shape. Map that practice design and engineering? What are roads using string. Determine a ratio for taking the paths of study and entry points into the field? measurements to scale, and mark intervals on How do these jobs require creative and collabor- the map accordingly. Using marbles as vehicles ative thinking similar to the artistic process? and cardboard (folded in a V shape) or pipe insulation (cut in half for a U shape) as roadways, experiment with dropping the “cars” onto the track.

Smoke, 1967, Tony Smith ______

TONY SMITH United States, 1912–1980 Smoke, 1967, fabricated 2005 Painted aluminum, installation; 290 x 564 x 396 in. LACMA, made possible by the Belldegrun Family’s gift to LACMA in honor of Rebecka Belldegrun’s birthday © Tony Smith Estate/ARS, NY (M.2010.49)

During the 1960s and ’70s, Tony Smith’s The individual parts of Smoke are machine-made, architectural artworks helped define “minimalism” but their configuration references shapes and in modern sculpture, which was concerned with forms inspired by life, such as a crystalline simplicity rather than ornamentation. Many of structure. The overall hexagonal formation his sculptures employ the triangle in complex mimics the shape of a honeycomb and points geometric patterns. In the sculpture Smoke, in to Smith’s fascination with natural enclosures.1 LACMA’s permanent collection, two basic triangular As with a cave, both positive and negative space units, a tetrahedron (a polyhedron or three- serve defining roles. The patterned absences or dimensional solid made of four triangular faces) gaps in space define the sculpture’s environment and an octahedron (formed by two tetrahedrons as much as the solid portions. Perhaps this is why opened at a vertex and conjoined), are scaled to Smith called his works “presences” rather than life size, repeated, and combined in a methodical sculptures, emphasizing the relationship between configuration. While the design is strictly pre- an artwork and its surrounding environment in scribed, the sculpture’s outline seems organic, the creation of a multidimensional experience. appearing curvilinear and growing both taller and wider, akin to the multidirectional path of billowing smoke as the viewer walks toward it, beneath it, and views it from above.

TONY SMITH United States, 1912–1980 Diagram of Cigarette, 1967 © Tony Smith Estate

The tetrahedron and octahedron (an eight-faced Point of Entry: Take a closer look at the diagram polyhedron) are modules, or basic units, that and chart the details that you see. How does it mark dominate much of Smith’s practice. “In my Smith’s mathematical thinking and artistic process? work,” he explained, “I use small cardboard Notice the overall form of the sculpture as well as maquettes [models], actual little tetrahedra the shape of the module. Each vertex is labeled a, b, and octahedra, and I paste them together with c, or d, forming a system to direct the connection of tape in order to arrive at the form of the work.”2 angular points. By rearranging the modules in various combinations until he reached a desired spatial effect, Essential Question: How do shapes combine to Smith not only determined the overall form but create sculptural forms inspired by life? the ratio between the two parts, such as three tetrahedra to every two octahedra. The ratio Grades: 6–10 presumably created a system for production that informed the execution of the final work. Core Content: Shape, module or fractal, vertex, polyhedron, volume, ratio, form, geometric and Smith explored this building process in a nearly organic, positive and negative space, maquette or thirteen-foot-tall “cave” constructed of three model, scale, and weight. thousand die-cut tetrahedra and fifteen hundred octahedra-shaped pieces of corrugated cardboard. Line of Inquiry: What do you notice about Smoke? For the sculpture’s installation, the cardboard die- Describe the basic unit that comprises this work. cuts were shipped flat to the installation site and How is it repeated and arranged to create a pattern? individually assembled and adhered together If you added more units to the pattern, what would according to Smith’s model. This and other works the progression of growth look like and where made of expendable materials have since been would the sculpture’s outer limits expand? If you destroyed. Some sketches, however, have remained, were to create a sculpture inspired by nature using such as this diagram for another Smith sculpture a pattern, what form would you choose? Visit a titled Cigarette. local park for inspiration.

Sketch a shape, then bring the sketch to class. Revision: If certain parts appear unstable, how will Examine the shape that you created and think you alter the weight distribution or stress to secure about how you might divide the shape into a the sculpture? If an alteration occurs to one piece, fractional representation. What is the basic unit how will it affect other pieces? Revisit the location that could comprise the overall form? How are where the sculpture will be installed. Does it fit the units joined? Is there a hidden shape at the aesthetically with its surroundings? How much junctures? Use toilet paper tubes or rolled news- material will be needed to execute a final version of paper as basic industrial units and experiment with the sculpture in metal, and at what cost? Include construction. Determine the points of intersection financial findings on the blueprint. and the secondary form (for example, a crumpled and compressed sheet of newspaper) that could be Presentation: Request permission to install the used to adhere two or more units at a vertex. As paper sculptures in the local park for one day. you build, count the ratio of primary to secondary Invite the city parks and recreation department units and document your plan as a blueprint. to attend the opening, and ask students to present the blueprints as new artwork proposals. Ask Equal Voicing: How will you work as a team department representatives to vote on the most to create the sculpture? Roles may include mathe- successful proposal, based on aesthetics and maticians to measure the units, draftsman to draw production costs. the blueprint, engineers to design construction, and preparators to execute the design. Researchers Reflection: Does math exist in nature? How do should determine the cost of reproducing the artists transform natural shapes into man-made paper units in metal, and accountants calculate forms? How do teams of people execute artworks? the total cost of building a final version in metal. How do other creative practitioners, such as designers and architects, find inspiration in nature?

TONY SMITH United States, 1912–1980 Diagram of Cigarette, 1967 © Tony Smith Estate

Levitated Mass, 2011, Michael Heizer ______

MICHAEL HEIZER United States, b. 1944 Levitated Mass, 2011 Granite, concrete, and steel; 258 x 5472 in., Zenith: 180 in., Weight: 340 tons LACMA © Michael Heizer (M.2011.35)

LACMA’s newest installation, Levitated Mass, connects Levitated Mass was originally conceived in 1969, the fields of math and engineering with art. Its during the land-art movement, and realized in creator, Michael Heizer, had visited archaeological 2011, after the perfect rock was identified to sites with his father, Dr. Robert Heizer, an archaeo- serve as the artwork’s specimen. The 340-ton logist who studied the transport of megarocks piece of granite was transported 106 miles from during antiquity. The concept of ancient cultures its home in a Riverside, California, quarry to its using technology to mark their place and time new installation at LACMA. At a height of 21½ feet, undoubtedly influenced Michael Heizer, who is the boulder sits along a 456-foot-long ramp cut considered to be an early land artist. The land-art into the museum’s Hancock Park lawn at a total movement of the 1960s and ’70s engaged the land depth and width of 15 feet, which allows crowds as a sculptural material, and often located artworks to walk directly underneath the giant rock. in nature.

MICHAEL HEIZER United States, b. 1944 Preliminary sketch for Levitated Mass, 2011 Courtesy of the artist © Michael Heizer

When Heizer identified the pyramidally shaped Nearly the width of three freeway lanes, the rock, he inspected it and took detailed measure- boulder was driven at just five to eight miles per ments. Construction workers used these hour over eleven consecutive days. dimensions to build the customized ramp out of concrete and reinforced steel, and designers used When the rock arrived at LACMA, a custom-built them to engineer the 294-foot-long, 32-foot wide crane lifted the rock into place. Granite land- by 23-foot-tall transporter to lift and carry the scaping and palm trees were added to reference rock. To move the rock, workers first dug beneath its original desert home. A band of steel encircles all of its sides and used hydraulic jacks to lift it. the installation, marking a slope that slowly Workers then assembled the carrier around the descends toward the ramp, giving visitors the rock to form the foundation of the transporter. opportunity to approach the rock from ground The carrier was designed with many pivot points level and even touch its surface. so that various sections could move independently.

Point of Entry: Levitated Mass is an example of others? Choose a large-scale object that exists on a site-specific installation, or an artwork in the your campus, such as an old bench or an unused form of an environment made with a particular bookcase. Consider where you might move this location in mind. Take a look at Heizer’s prelim- object, whether to the playground or the library. inary sketch. How did he consider the museum Calculate the distance it must travel and the force campus when planning for the installation? required to move it. Generate a list of technologies What evidence can you find to support your or resources needed for the transport. How will claim? Installation art often engages the viewer you prepare the new site? What will you add to in a sensory experience. What might it feel like transform this object and site into a functional art to walk underneath Levitated Mass? How would installation? the experience change under a larger or smaller rock, or an entirely different object? Equal Voicing: How will the class work as a team to install the object? Roles may include engineers Essential Question: How do artists connect math, to plan the transport, preparators to execute the engineering, and technology to create sculptural installation, and sculptors to re-envision the installations? surrounding environment to enhance the installation’s look and feel. Grades: 8–12 Revision: Perhaps this object has previously Core Content: Weight, displacement, balance, gone unnoticed. How will students and teachers force, mass, density, volume, dimensions, gravity, interact with it now? What will you need to distance. enhance the object and site? Identify source materials that complement the look, feel, and Line of Inquiry: What surprises you about function of your installation, such as books or Levitated Mass? What questions do you have for seating to turn the old bookcase into an the artist? For the mathematician or the engineer? interactive library site. How can you calculate the amount of force (mass multiplied by speed) required to move this mass Presentation: Invite members of the school, a specific distance? Considering the amount of neighborhood, and professional community with energy and coordination required to move the whom students interacted over the course of the rock, what might the impact be of moving several previous units to view the campus installations. rocks of this scale to a single location? What tools Present the preliminary studies that informed would be necessary for such transport? the artwork.

Experiment with the transport of objects of Reflection: What are the similarities and varying weight and scale, from a marble to a differences between artistic, mathematical, and gallon of water, a projector, a desk, or a television. engineering practice? What is the value of each What technology could aid in the transport to society? Why is it beneficial for artists, process? How could you enlist the expertise of mathematicians, and engineers to work together?

______

Use LACMA as a resource for your PBL instruction. Consider launching your unit by visiting the Compare the images on the following pages with: museum with your class as an interactive entry- point activity. • twenty-four-hour video of Urban Light (included on the curriculum CD) When designing your own PBL units of instruction, consider using the brainstorming • a spotlight video of Metropolis II template and project calendar provided to plan (http://lacma.wordpress.com/2012/01/10/ and facilitate the experience. Research artworks metropolis-ii) from LACMA’s permanent collection to serve as inspiration (www.lacma.org/art/collection). If you • time-lapse images of Smoke’s construction share students with another instructor, perhaps (www.lacma.org/video/time-lapse-images- divide the work by pairing up with a colleague so smoke) that, for instance, the math teacher handles math instruction and the art teacher facilitates the art- • multimedia documentation of Levitated Mass making. Build in as many opportunities as to track the rock’s transport (http://www. possible to share student work with classmates, lacma. org/video/levitated-mass). faculty, administrators, and the Education Department at LACMA.

1 Jane Livingston, “Tony Smith” in A Report on the Art and Technology Program of the Los Angeles County Museum of Art, 1967–1971, pp. 307–8.

2 Jane Livingston, “Tony Smith,” p. 309.

These curriculum materials were prepared by Jennifer Reid, Kiffen Madden-Lunsford, George Crowder, and Holly Gillette and designed by Jenifer Shell. © 2013 Museum Associates/LACMA. All rights reserved.

Evenings for Educators is made possible by , The Rose Hills Foundation, the Thomas and Dorothy Leavey Foundation, and the Kenneth T. and Eileen L. Norris Foundation.

Education programs at the Los Angeles County Museum of Art are supported in part by the City of Los Angeles Department of Cultural Affairs, the William Randolph Hearst Endowment Fund for Arts Education, and Rx for Reading.

CHRIS BURDEN United States, b. 1946 Urban Light, 2008 202 restored cast-iron antique street lamps, 320½ x 666½ x 704½ in. LACMA, the Gordon Family Foundation’s gift to Transformation: The LACMA Campaign © Chris Burden (M.2007.147.1–.202)

CHRIS BURDEN United States, b. 1946 Urban Light (detail), 2008 202 restored cast-iron antique street lamps, 320½ x 666½ x 704½ in LACMA, the Gordon Family Foundation’s gift to Transformation: The LACMA Campaign © Chris Burden (M.2007.147.1–.202)

CHRIS BURDEN United States, b. 1946 Metropolis II, 2010 3½ hp DC motors with motor controllers, 12,000 custom manufactured die-cast cars (1,100 for operating, 10,900 for replenishing damaged cars), 26 HO-scale train sets with controllers and tracks (13 for operating,13 for replenishing damages), steel, aluminum, shielded copper wire, copper sheet, brass, various plastics, assorted woods and manufactured wood products, Legos, Lincoln Logs, Dado Cubes, glass, ceramic and natural stone tiles, acrylic and oil-based paints, rubber, and sundry adhesives; 117 x 339 x 230 in. © Chris Burden. Courtesy Gagosian Gallery. Photography by E. Koyama. (L.2010.33.1)

MICHAEL HEIZER United States, b. 1944 Levitated Mass, 2011 Granite, concrete, and steel; 258 x 5472 in. Zenith: 180 in., Weight: 340 tons LACMA © Michael Heizer (M.2011.35)

MICHAEL HEIZER United States, b. 1944 Megalith slated to become part of Michael Heizer’s Levitated Mass, prepared for transport from quarry in Riverside County to the Los Angeles County Museum of Art, 2012 2012 © 2012 Michael Heizer, photo by Tom Vinetz

Name:

Artwork in Focus:

Essential Question:

Core Content:

Line of Inquiry:

Equal Voicing:

Revision:

Presentation:

Reflection:

Name:

Page 1

Driving Question:

Monday Tuesday Wednesday Thursday Friday

Goals:

Monday Tuesday Wednesday Thursday Friday

Goals:

Name:

Page 2

Driving Question:

Monday Tuesday Wednesday Thursday Friday

Goals:

Monday Tuesday Wednesday Thursday Friday

Goals:

Classroom Activity

Building a Metropolis

______

Essential Questions What forms serve as the building blocks for a metropolis? How do artists and mathematicians design the built environment?

Grades 3–6

Time Two to four class periods

Art & Math Concepts Form, interval, grid, quadrant, space, sculpture

Materials Colored masking tape, measuring tape, cardboard, a variety of recycled materials (cardboard cylinders, packing material, plastic containers, bottle caps, etc.), glue, scissors, white and colored tempera paint, brushes, water, paper towels. Optional: construction paper, wooden dowels or sticks.

Talking about Art View and discuss the photographs and engineering map of Chris Burden’s Metropolis II (2011) included in the printed and digital curriculum. Watch the spotlight video of Metropolis II on Unframed The LACMA Blog at http://lacma.wordpress.com/2012/01/10/ metropolis-ii.

What are the first words that come to mind when you see Metropolis II? What three-dimensional forms, such as cubes, cylinders, or spheres, do you see? How are the forms arranged to create a city? What other urban elements do you notice? What is the relationship between the building forms and the freeway tracks? How are they integrated into the overall design?

How does looking at photographs of Metropolis II compare with watching a video of the sculpture? What did you notice about the artwork from the video that you did not notice in the photographs? What do you think it might look, sound, and feel like to experience Metropolis II as a miniature resident? How would it compare to living in a life-size city?

An engineer worked alongside the artist to design and build Metropolis II. First, the engineer sketched a simple two-dimensional shape to represent the base of the sculpture. Then, he mapped out the track configurations using string and pen. He marked the string tracks with pen at five-foot scale intervals to guide construction. Lastly, artists added wooden and tiled buildings in between the tracks to mimic the look and feel of a real city. How does Metropolis II compare with the look and feel of your neighborhood? How would you describe the natural landscape of the community? How would you describe the man-made or built environment? What three-dimensional forms comprise these types of environments?

Making Art Create a classroom metropolis by, first, analyzing a map of the school neighborhood. What landmarks surround the school? What buildings, roadways, bridges, and parks do you notice? Visit some of these structures and sketch the forms that they take (rectangular, triangular, spherical, etc). If you could add forms, structures, or other elements to the neighborhood, what would you add and why?

Place four large pieces of cardboard on the classroom floor, creating four equal quadrants. Lay a simple city grid on top of the cardboard using colored masking tape. Use one color to map north-south thoroughfares and another color to map east-west streets. Keep the map simple, leaving negative space or plots of land in between roads. Divide students into four groups, assigning each group a different quadrant to build. They can use the cardboard as a base to adhere recycled sculptural materials. Forms such as rectangular prisms and cylinders should represent the different structures or spaces that they would add to the neighborhood. Encourage them to work with large forms first, then add smaller forms as details later.

When construction is complete, whitewash the entire city with quick- drying white tempera paint. When dry, add windows, doors, and signage using tempera colors. Use colored construction paper, dowels or sticks, and other recycled materials to add trees, plants, and flowers to the natural landscape. Students can also bring toy cars or toy people from home to turn the sculpture into a full-fledged city.

Reflection Move the entire sculpture into the auditorium and invite the school community, including local politicians, city planners, and neighborhood council members, to a city ribbon-cutting ceremony. Ask students to reflect on how they used the languages of art and math to build their city, and to share their experience with the professionals in attendance.

Curriculum Connection Analyze the local city council district’s land use map with students. What resources (housing, work, recreation, and transportation) are currently available to residents? What needs will arise in the future? How can artists, mathematicians, engineers, and environmental scientists address these needs together?

Evenings for Educators, Building STEAM: Art, Math, and Technology. April 2013. Prepared by Tom Miller with the Los Angeles County Museum of Art Education Department.

Classroom Activity

2-D to 3-D Symmetry

______

Essential Question How do artists use geometry and symmetry to create two- and three-dimensional compositions?

Grades K–3 & Special Day Classes

Time One class period

Art & Math Concepts Line, shape, form, two and three dimensions, positive and negative space, symmetry, balance, composition

Materials Pencil, colored construction paper, scissors, glue, rulers. Optional: cardboard.

Talking about Art View and discuss the photographs and planning diagrams of Chris Burden’s Urban Light (2008) included in the printed and digital curriculum. Watch the time lapse video of Urban Light from day to night included on the curriculum CD.

What do you notice about Urban Light? Describe the lines that you see. Are they straight or curvy? How are the lines arranged? What more can you find, including shapes (two-dimensional) and solids (three-dimensional forms)? The arrangement of lines, shapes, or solids in an artwork is called composition. What are some words to describe this composition? The lines, or lampposts, are arranged to create symmetry. With your hand, draw the composition’s line of symmetry in the air. Can you estimate the number of lamps on either side?

Gather students and stand together in a circle. Ask one student to join the center of the circle and lift their arms up like the letter “T,” to establish the line of symmetry. Next, ask two volunteers to create lines with their bodies and place themselves on either side of the line of symmetry. Are you a curvy or straight line? Have volunteers join two at a time to add to the composition. Are everyone’s lines symmetrical? What do you need to change to create a symmetrical composition?

Burden arranged Urban Light’s 202 antique lampposts symmetrically by installing them carefully on a grid. Do you notice any patterns in the arrangement? Lamps of the same design are grouped together and the groups are ordered by height, to create three-dimensional symmetry in the form of a pyramid.

Making Art Create a symmetrical collage by folding a piece of construction paper vertically or horizontally, to create a line of symmetry. Open the paper and lay it flat on the table.

Cut pairs of geometric shapes out of construction paper. To create two identical shapes, fold a piece of construction paper in half, draw a simple shape such as a triangle or square on one side, then cut along the drawn lines. For younger students, you can also prepare stencils by cutting shapes out of cardboard for students to trace. When you have gathered a variety of shapes, start arranging them on one side of the line of symmetry. When you have reached a desired arrangement, glue them down with a glue stick. Complete the composition by carefully matching shapes and laying them on top of each other. Then, put a small dab of glue on top of each shape and carefully fold the paper again. Open the paper to reveal a perfectly symmetrical composition.

For older students, build on two-dimensional symmetry by adding three-dimensional elements. Measure and cut a variety of strips using a ruler then fold the strips to create texture. Next, arrange the strips so that they connect similar shapes on either side of the line of symmetry, turning the collage into a symmetrical paper sculpture.

Reflection Turn to a partner and share one thing that you like about your collage. Ask older students to talk about the process of rearranging the composition to reach symmetry. Then, share artworks with the class by answering these questions: What types of lines and shapes did you use? What colors did you use and why? Point out two parts of the composition that exemplify symmetry.

Curriculum Connection As a team, measure the height of three or more items in the classroom using a ruler. Arrange the items according to length or height. Collect doubles of each item, identify a line of symmetry, and then arrange the items symmetrically as Burden did in Urban Light.

Evenings for Educators, Building STEAM: Art, Math, and Technology. April 2013. Prepared by Judy Blake with the Los Angeles County Museum of Art Education Department.

Classroom Activity

Levitating a 25-lb Mass ______

Essential Question How do artists create art installations using engineering concepts?

Grades 9–12

Time Two to three class periods

Art & Math Concepts Estimation, structural engineering, weight-bearing technology, balance, illusion, installation

Materials Paper, pencil, popsicle sticks, wood glue, objects weighing at least 25 pounds (i.e., rock, cinder block, brick, watermelon). Optional: blueprint paper.

Talking about Art View and discuss the photographs and preliminary sketch of Michael Heizer’s Levitated Mass (2012) included in the printed and digital curriculum. Watch documentation of the megalith’s planning, transport, and installation from LACMA’s Video Library at https://www.lacma.org/video/levitated-mass.

What questions do you have about Levitated Mass? If you could, what would you ask the artist and the engineer about the planning, transport, and installation of this work?

Heizer conceived of this monumental sculpture in 1969. At a Riverside, California quarry 40 years later, he identified the perfect rock to serve as the artwork’s specimen. First, mathematicians studied the rock, taking detailed measurements. Based on these measurements, engineers designed a massive transporter to carry the rock and construction workers used hydraulic jacks to lift it. To ensure a safe journey to LACMA, city planners devised a travel route, identifying bridges and streets that could accommodate the rock’s 340-ton weight. It traveled for 10 days over 100 miles, spanning 4 counties and 22 cities before it arrived at Hancock Park. A custom-built crane lifted the rock into place, on top of a ramp made of concrete and reinforced steel. Lastly, granite landscaping and palm trees were added to reference the rock’s desert home. It is Heizer’s close attention to the rock and its surrounding environment that transformed this artwork and engineering feat into a sculptural installation.

Making Art Installations are artworks that take the form of three-dimensional environments. Create your own installation that explores art and engineering concepts of weight and levity by, first, splitting into groups of two to three. Decide who will take the role of artist, mathematician, and engineer and how you will work together to “levitate” a 25-pound mass using just popsicle sticks and glue.

Analyze the challenge at hand by brainstorming engineering designs. Designs that employ triangles and pyramids, shapes and forms with a heavy base and a pinnacle on top, disperse pressure and provide strength and stability. The ultimate goal is to build structural integrity using as few sticks as possible. Have team members work together to create sketches of possible supports with the above limitations. Then, estimate the number of sticks required for execution. Remember, you must use whole sticks as the building units.

Next, transform the sketches into three-dimensional supports. Experiment by testing out your design and making needed adjustments. You can use combinations of triangles and squares to make any geometric solid (e.g., square pyramid, triangular pyramid, trapezoidal prism, etc.). Work together to glue the final configuration.

When finished, engineers should ensure that the adhesives and sticks are structurally sound. Mathematicians should write an equation for calculating the total number of sticks. Artists should document the final arrangement on a sheet of blueprint paper. Allow the structure to dry overnight then work as a team to lift the 25-pound mass into place. Take a look from many angles. Does the rock appear to levitate?

Reflection Does the final design match the original sketch? If not, what changes did you make along the way? How did you work together to complete the challenge?

Place the results of your experiment outside on the school campus. What can you add to transform the levitating rock into a miniature art installation? Document your installation by photographing it from different angles in the sunlight.

Curriculum Connection Compare the number of sticks it took to levitate the mass with your original estimate. How accurate was your prediction? If you were to double the weight of the mass, how many more sticks might you need? Try calculating the total number of sticks in different weight and pressure scenarios.

Evenings for Educators, Building STEAM: Art, Math, and Technology. April 2013. Prepared by Tom Miller with the Los Angeles County Museum of Art Education Department. Classroom Activity

Straw Polygon Sculptures

______

Essential Questions How do artists find inspiration in nature and math? How do they build patterned forms using three-dimensional units?

Grades 6–9

Time One to two class periods

Art & Math Concepts Line and shape, organic and geometric, polygon, form, polyhedron, volume, space, balance

Materials Pens, rulers, protractors, compass, plastic drinking straws, paper clips or fasteners, rubber bands, duct tape, cardboard. Optional: air-drying clay, construction paper, colored tape, hot glue

Talking about Art View and discuss the photographs of Tony Smith’s Smoke (1967, fabricated 2005) and the artist’s diagram included in the printed and digital curriculum. Watch the time lapse video of Smoke’s construction from LACMA’s Video Library at www.lacma.org /video/ time-lapse-images-smoke.

Take a look at the sculpture from multiple viewpoints. What shapes and forms do you notice? Are they curvy shapes or angular forms? In art, curvy shapes are described as organic because they mimic shapes from life, while angular shapes are called geometric because they exemplify mathematical concepts. Do these mathematical shapes remind you of forms from life?

Smith was known for his minimalist sculptures that employ simple shapes in elaborate construction. The sculpture’s outline appears organic, but the individual parts that comprise the structure are geometric.

Two basic polyedra or triangular units—a tetrahedron (a three- dimensional solid made of four triangular faces) and an octahedron (formed by two tetrahedrons opened at a vertex and conjoined)— are scaled to life size, repeated, and combined to make up Smoke’s frame. The overall hexagonal formation references the shape of a honeycomb, pointing to Smith’s fascination with positive and negative space and porous forms from life.

Making Art Using a pen and a photocopy of Smoke, circle the following geometric shapes: square, rectangle, triangle, hexagon (6-sided polygon), octagon (8-sided polygon), and nonagon (9-sided polygon). Are they uniform or irregular shapes?

In small groups, use plastic drinking straws to create a simple polygon. Choose from a variety of materials to connect the straws together, such as rubber bands, clay, paper clips or fasteners, and duct tape. Create a replica of the polygon to serve as the base for a sculpture then produce more polygons to use as building units. Connect the units together or build outward from one unit, both vertically and horizontally, to create a pattern in three dimensions. If necessary, adhere the sculpture with hot glue for structural reinforcement and attach to a cardboard base.

Now that students have created a strict patterned sculpture, ask older students to experiment with form and balance by creating a free-form organic sculpture. Divide students into groups of three and ask each to use straws and adhesives to create a free-form unit. When finished, experiment with attaching the three units together, ensuring balance and structural integrity, to create a collaborative work of art.

Reflection Display patterned and free-form sculptures together in the classroom and facilitate a gallery walk. View sculptures from above and below, and from many different perspectives. Are the individual units that comprise the patterned sculptures regular? When you walk around a free-form sculpture, how does the outline change and transform? Compare and contrast the different works. Which do you prefer and why?

Ask each group to take their collaborative sculpture and install it in a location on the school campus. Lead a walking tour of all of the sculptures and note, in a sketchbook, the different shapes that you see, such as triangles, hexagons, octagons, and nonagons. Draw a sketch of each sculpture within its natural environment. Are any shapes or forms reflected in the landscape around it?

Curriculum Connection Revisit the patterned sculpture and measure one of its individual units. Using these measurements, calculate the total volume of the sculpture. Then, work together as a team to calculate the volume of the free-form sculpture.

Evenings for Educators, Building STEAM: Art, Math, and Technology. April 2013. Prepared by Helen Marish with the Los Angeles County Museum of Art Education Department.

Building STEAM: Art, Math, and Technology

Selected Resources

Online Resources Related Curriculum Materials ______

A Report on the Art and Technology Program Evenings for Educators resources include an Los Angeles County Museum of Art illustrated essay, color images, classroom www.lacma.org/art/reading-room activities, and related resources. Printed Read about the history of LACMA’s commitment curriculum is available through LACMA’s to technology through the Art + Technology Education Department or browse selected Program of 1967–71, which paired contemp- curricula online at www.lacma.org (Programs/ orary artists with the industrial and scientific Education/Evenings for Educators). communities of Los Angeles. Access the report on the Pacific Standard Time tab. Preserving the Past: Conservation at LACMA December 1995 STEAM Education Resource Center PBS Teachers Art, Ecology, and the Environment www.pbs.org/teachers/stem May 1997 Explore STEM lesson plans such as “Heavy Lifting,” a challenge to design and build a crane The Visible World: Observation in Art and Science out of recycled materials by experimenting with April 1999 the properties of weight and force. Wonderment and Interaction: Science, Technology MIT+K12 and Art Massachusetts Institute of Technology February 2004 http://k12videos.mit.edu Use MIT’s collection of K–12 student-focused The Urban Environment in Art videos as classroom teaching tools. Search by March 2006 grade level or subject area, or create and upload your own video assignments.

MIT App Inventor Massachusetts Institute of Technology http://appinventor.mit.edu/teach Take STEAM Education into the digital age by teaching students how to design an app. Use the curriculum and media library to find lesson plans and visual aids.

Books for Teachers Books for Students ______

Hallermann, Sara, John Larner, and John R. Moscovich, Ivan. The Big Book of Brain Games: 1,000 Mergendoller. Project-Based Learning in the PlayThinks of Art, Mathematics, and Science. Elementary Grades. Novato: Buck Institute of New York: Workman Publishing Company, Education, 2011. 2006. A practical guide to Project-Based Learning A collection of brainteasers that test visual (PBL), designed for K–5 teachers. Contains and problem-solving skills using numbers, project planning, assessment, and patterns, geometry, logic, and probability. management tools as well as sample projects from different grade levels and Ruffler, Walter. Paper Models that Move: 14 subject areas. Ingenious Automata and More. Mineola: Dover Publications, 2011. Larner, John. Project-Based Learning Starter Kit. A world of paper engineering through Novato: Buck Institute of Education, 2009. projects that explore levers, gears, cranks, Tools and tips for PBL in the middle- and and other devices. high-school years. Includes project-ready rubrics and links to online resources. Salvadori, Mario. The Art of Construction: Projects and Principles for Beginning Engineers and Riley, Susan M. STEAM Point: A Guide to Integrating Architects. Chicago: Chicago Review Press, Science, Technology, Engineering, the Arts, and 2000. Mathematics through the Common Core. The basic principles of construction for Seattle: CreateSpace Independent all types of urban structures, including Publishing, 2012. bridges, skyscrapers, and other A guide for teachers and administrators architectural works. Projects employ on STEAM and Common Core State accessible everyday materials. Standards integration. Tang, Greg. The Art of Problem-Solving. New York: Sousa, David A. From STEM to STEAM: Using Brain- Scholastic Press, 2003. An exploration of Compatible Strategies to Integrate the Arts. four basic rules in problem-solving through Thousand Oaks: Corwin, 2013. works of art: keeping an open mind, Techniques, lesson plans, and templates looking for unusual number combinations, to help educators integrate artmaking into using multiple skills, and looking for daily instruction, building skills critical to patterns. STEM Education. Woods, Michael. Ancient Machine Technology: From Wheels to Forges. Minneapolis: Twenty- First Century Books, 2011. A history of the evolution of technology through the work of ancient artisans to contemporary engineers.